Tag: coding

Blog Entry Monday, June 24, 2024 (c) James Pate Williams, Jr. Computing Binomial Coefficients and Pascal’s Triangle in the C Language

Enter n (<= 18) below:
5

Enter k (<= 18) below:
0

1       1

Enter n (<= 18) below:
5

Enter k (<= 18) below:
1

5       5

Enter n (<= 18) below:
5

Enter k (<= 18) below:
2

10      10

Enter n (<= 18) below:
0
Enter n (<= 18) below:
0

Pascal's Triangle:

    1
    1     1
    1     2     1
    1     3     3     1
    1     4     6     4     1
    1     5    10    10     5     1
    1     6    15    20    15     6     1
    1     7    21    35    35    21     7     1
    1     8    28    56    70    56    28     8     1
    1     9    36    84   126   126    84    36     9     1
    1    10    45   120   210   252   210   120    45    10     1
    1    11    55   165   330   462   462   330   165    55    11     1
    1    12    66   220   495   792   924   792   495   220    66    12     1
    1    13    78   286   715  1287  1716  1716  1287   715   286    78    13     1
    1    14    91   364  1001  2002  3003  3432  3003  2002  1001   364    91    14     1
    1    15   105   455  1365  3003  5005  6435  6435  5005  3003  1365   455   105    15     1
    1    16   120   560  1820  4368  8008 11440 12870 11440  8008  4368  1820   560   120    16     1
    1    17   136   680  2380  6188 12376 19448 24310 24310 19448 12376  6188  2380   680   136    17     1
    1    18   153   816  3060  8568 18564 31824 43758 48620 43758 31824 18564  8568  3060   816   153    18     1

C:\Users\james\source\repos\BinomialCoefficeint\Debug\BinomialCoefficeint.exe (process 40028) exited with code 0.
Press any key to close this window . . .
// BinomialCoefficient.c (c) Monday, June 24, 2024
// by James Pate Williams, Jr. BA, BS, MSwE, PhD

#include <stdio.h>
#include <stdlib.h>
typedef long long ll;

ll** Binomial(ll n)
{
    ll** C = (ll**)calloc(n + 1, sizeof(ll*));

    if (C == NULL)
        exit(-1);

    for (int i = 0; i < n + 1; i++)
    {
        C[i] = (ll*)calloc(n + 1, sizeof(ll));

        if (C[i] == NULL)
            exit(-1);
    }

    if (n >= 0)
    {
        C[0][0] = 1;
    }

    if (n >= 1)
    {
        C[1][0] = 1;
        C[1][1] = 1;
    }

    if (n >= 2)
    {
        for (int i = 2; i <= n; i++)
        {
            for (int j = 2; j <= n; j++)
            {
                C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }
    }

    return C;
}

ll Factorial(ll n)
{
    ll fact = 1;

    if (n > 1)
    {
        for (int i = 2; i <= n; i++)
            fact = i * fact;
    }

    return fact;
}

ll BC(ll n, ll k)
{
    return Factorial(n) / (Factorial(n - k) * Factorial(k));
}

int main()
{
    int i = 0, j = 0;
    ll** C = Binomial(20);

    while (1)
    {
        char buffer[256] = { '\0' };
        
        printf_s("Enter n (<= 18) below:\n");
        scanf_s("%s", buffer, sizeof(buffer));
        printf_s("\n");

        ll n = atoll(buffer);

        if (n == 0)
            break;

        printf_s("Enter k (<= 18) below:\n");
        scanf_s("%s", buffer, sizeof(buffer));
        printf_s("\n");

        ll k = atoll(buffer);
                
        printf_s("%lld\t%lld\n\n", C[n + 2][k + 2], BC(n, k));
    }

    printf_s("Pascal's Triangle:\n\n");

    for (i = 2; i <= 20; i++)
    {
        for (j = 2; j <= 20; j++)
            if (C[i][j] != 0)
                printf_s("%5lld ", C[i][j]);

        printf_s("\n");
    }

    for (i = 0; i <= 20; i++)
        free(C[i]);

    free(C);
}